Preparation

1. In a blender, puree the parsley leaves and stems, lemon zest and juice, and eggs until only specks of parsley remain. Pour into a bowl. Add the milk to the blender. Swirl the milk around to incorporate any remaining parsley puree. Mix the flour into the parsley puree, then mix in the milk; season the batter with 1/2 tsp. salt and 1/4 tsp. pepper. Let stand at room temperature for 15 minutes.

2. Meanwhile, bring a large pot of water to a boil. Prepare a large bowl of ice water. Reduce heat under the pot so the water gently simmers. Working in 3 batches (about 3/4 cup of batter at a time), hold a colander, or a potato ricer fitted with the disk with the largest holes, over the water and, using a silicone spatula, push the batter through the colander so it falls into the water. Cook the spaetzle until they rise to the top, about 2 minutes; using a slotted spoon, transfer to the ice water. Repeat with the remaining batter. When all the spaetzle are cool, drain and transfer to a medium bowl. Drizzle with EVOO; toss until coated. (The spaetzle can be covered and chilled for up to 3 days.)

3. In a large skillet, melt the butter with the olive oil over medium-high heat. Add the mushroom; cook, stirring often, until browned, about 5 minutes. Add the garlic; cook, stirring often, until aromatic, about 1 minute more. Add the spaetzle; cook, stirring often, until lightly browned, about 8 minutes. Top with the chopped parsley and cheese.